Is it consistent to be a libertarian while opposing suicide on moral grounds?

I'm no expert on libertarianism in political philosophy, but I think I can answer this one: Yes.

As I understand it, political libertarianism is a position concerning the legitimate power of the state. One can consistently oppose suicide on moral grounds while maintaining that the state has no business interfering with suicide. One can consistently think that, for various reasons, one morally ought not commit suicide while also thinking that the law should keep out of it. Indeed, a particularly strong distinction between "immoral" and "illegal" seems to lie at the heart of the libertarian outlook.

Typically, a libertarian (in the domain of politics; "libertarian" is also the label for someone who adopts a view in philosophy of mind or action theory involving free will) is someone who believes that societies should have a government that is the smallest possible in order to protect certain basis rights (perhaps a proper government should, on the grounds that persons have the right to life, prohibit murder and seek to prevent it). A libertarian might (on rare occasions) support some publicly funded health care, but he or she would (ideally) like such matters to be funded by individuals voluntarily by the individuals themselves. So, what about libertarians and suicide? If the libertarian believes that a minimal government should prohibit and prevent murder and she believes that suicide is wrong because it is a case of self-murder, then she may consistently support the government's prohibition and prevention of suicide. However, she may be "opposing suicide on" different moral grounds, e.g. she thinks it is prohibited by God or she thinks that in almost all cases suicide is ruled out on Kantian or utilitarian grounds. For the most part, libertarians do not think these religious or philosophical judgments of these kinds should be employed by the state to control its citizens. So, in this case when suicide is deemed wrong but not as grave a wrong as murder, a libertarian may well contend that suicide is indeed wrong (persons who commit suicide are doing something morally wrong), only adding that it is not within a government's right to make suicide illegal.

There is one additional side to things: while a libertarian may oppose there being an overall, federal government that makes suicide illegal (assuming suicide is not self-murder), her moral objections to suicide may motivate her to join a society voluntarily that makes suicide prohibited. Without knowing the details, I imagine that most Christian monasteries and Muslim communities have rules that forbid suicide (e.g. they would not fund or support the "physician-assisted suicide" of one of its members). A libertarian might join some such organization while still not supporting a governmental prohibition of suicide.